If a variable takes the discrete values alpha | vedclass

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Question

(D) First,arrange the given $8$ values in ascending order:
$\alpha - 4, \alpha - 3.5, \alpha - 3, \alpha - 2.5, \alpha - 2, \alpha - 0.5, \alpha + 0.

Vedclass · Accepted Answer

$\alpha - \frac{9}{4}$

Vedclass · Answer

(D) First,arrange the given $8$ values in ascending order:
$\alpha - 4, \alpha - 3.5, \alpha - 3, \alpha - 2.5, \alpha - 2, \alpha - 0.5, \alpha + 0.5, \alpha + 5$
Since the number of observations $n = 8$ (which is even),the median is the average of the $4^{th}$ and $5^{th}$ terms.
$4^{th} 	ext{ term} = \alpha - 2.5 = \alpha - \frac{5}{2}$
$5^{th} 	ext{ term} = \alpha - 2$
$	ext{Median} = \frac{(\alpha - \frac{5}{2}) + (\alpha - 2)}{2}$
$	ext{Median} = \frac{2\alpha - 4.5}{2} = \alpha - 2.25 = \alpha - \frac{9}{4}$

Height (in $cm$)	$160$	$150$	$152$	$161$	$156$	$154$	$155$
No of students	$12$	$8$	$4$	$4$	$3$	$3$	$7$

If a variable takes the discrete values $\alpha - 4, \alpha - \frac{7}{2}, \alpha - \frac{5}{2}, \alpha - 3, \alpha - 2, \alpha + \frac{1}{2}, \alpha - \frac{1}{2}, \alpha + 5$ (where $\alpha > 0$),then the median is:

Similar Questions

What is the value of $x$ if the mean of $8, 6, 7, 5, x,$ and $4$ is $7$?

The following data gives the distribution of height of students. The median of the distribution is:

Height (in $cm$) $160$ $150$ $152$ $161$ $156$ $154$ $155$

No of students $12$ $8$ $4$ $4$ $3$ $3$ $7$

The mean of $50$ observations is $36$. If two observations $30$ and $42$ are removed,what is the mean of the remaining observations?

The number of observations in a group is $40$. If the average of the first $10$ observations is $4.5$ and the average of the remaining $30$ observations is $3.5$,then the average of the whole group is:

The relation between the median $M$,the second quartile ${Q_2}$,the fifth decile ${D_5}$,and the $50^{th}$ percentile ${P_{50}}$ of a set of observations is:

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